(a)We defined statistical numbers of degrees of freedom (NDF) as an equivalent uncorrelated number of points per unit area in a 2-dimensional random field.(b)The first order NDF is equal to Fisher's information about the first statistical moment. The second order NDF is an approximation of Fisher's information about the second moment.(c)Many interesting features of a random field and a random process were deduced from the NDF's. They are correlation time, correlation length, correlation area, line-correlation, area-correlation, and bundle-correlation.(d)The mutual information and the vector correlation coefficient between two random processes are useful to measure how they are globally correlated. Relationship between mutual information and vector correlation were investigated both theoretically and numerically.(e)The results obtalned above were applied to annualizing some meteorological data and biomedical data.6. 2つの時系列間の相互情報量やベクトル相関係数はこれらの大域的相関の強さを表すのに有用である。本研究ではこれらのふたつの間の関係を検討し、かつ、単位時間当たり相互情報量と単位長さ当たりのベクトル相関係数を定義し、これらの関係を明らかにした。7. 上記の成果をいくつかの気象データと生体信号解析に応用しそれらの解析を試みた。